Seismic Analysis of Water Supply Systems by Earthquake Scenario ...

SEISMIC ANALYSIS OF WATER SUPPLY SYSTEMS BY EARTHQUAKE
SCENARIO SIMULATION
Gee-Yu LIU, Chin-Hsun YEH, Hsiang-Yuan HUNG and Kuang-Wu CHOU
National Center for Research on Earthquake Engineering, Taiwan
ABSTRACT: In the past decade, scenario simulation has played a more and more important role in urban
earthquake hazard mitigation and emergency response. Both public and private sectors can be enhanced in
terms of their seismic preparedness and operation if adequate implementation of seismic scenario simulation
can be employed. Regarding water utilities, system-wide retrofit and emergency planning can be conducted
to reduce the likely damage and losses prior to the occurrence of a devastating earthquake. Post-earthquake
repair personnel and material dispatching, temporary water supply for affected people, emergency water
supply for hospitals and fire fighting, strategies for restoration and recovery can all benefit from
scenario-based analyses. In this research work, efforts were made to study and integrate pivotal technologies
essential to the earthquake damage and serviceability analysis of water systems, such as seismic hazard
analysis, empirical formulae for pipe repair rates, hydraulic analysis of water network system in terms of
pressurized pipe flow simulation, hydraulic models for various types of pipe damages, and Monte Carlo
method for the performance analysis of large and complicated systems. The water system in Yi-lan County,
Taiwan was selected as a test bed for the demonstration of its seismic serviceability analysis under an M7.1
earthquake scenario.
KEYWORDS: water system, post-earthquake performance, scenario simulation
1. INTRODUCTION
Water systems are one of the most essential
infrastructures in modern societies. The disruption of
water supply following earthquakes may cause
serious inconvenience to the daily life of people in
the disastrous areas. Medical caring, sanitation,
fire-fighting and so forth may be seriously affected,
too. It is very important to facilitate water utilities
with a seismic scenario simulation tool for help
estimate the likely service disruption following
earthquakes. Such tool will benefit the efforts to
improve preparedness, robustness, and resilience of
water systems in a quantitative approach. In the past
years, Shinozuka et al. (1981), Ballantyne et al.
(1990) and Markov et al. (1994) have made pioneer
studies in this topic. Recently, software called
GIRAFFE (Graphical Iterative Response Analysis
for Flow Following Earthquakes) has been
developed at Cornell University (2008). It was
successfully adopted as a decision support tool for
hazard mitigation and emergency response by the
Los Angele Department of Water and Power. It
employs EPANET as the engine for hydraulic
computation. EPANET is public computer codes
released by the Environmental Protection Agency,
U.S., especially for the solution of pressurized pipe
flow problem (Rossman, 2000).
Similar to GIRAFFE, a technology for assessing

the post-earthquake performance of water systems
has been developed at NCREE (Liu et al., 2010 &
2011). It consists of several steps, as depicted in
Figure 1. (1) estimate the seismic hazards (ground
shaking and failure) of where the interested water
network system locates, (2) simulate the locations of
pipe damages according to the hazards and pipe
repair rates (numbers of repairs per unit pipe length
caused by ground shaking and deformation,
respectively), (3) classify the properties of each pipe
damage (whether a break or a leak, and what which
model of pipe leak if it is a leak; the probability
model for pipe damages employed by GIRAFFE was
adopted here), (4) modify the hydraulic model of the
water network system to take into account the pipe
damages, (5) execute EPANET and take out the
water supply nodes affected by negative pressure
from the solution. Details of these steps will be
explained in the following sections.
EQ source parameters
ground motion attenuation
site effect
fault rupturing model
liquefaction susceptibility
liquefaction settlement model
pipe repair rate
pipe damage locating algorithm
equipment vulnerability
power outage
…
pipe damage hydraulic models
EPANET software
pre- and post-processors
EQ Event
Seismic Hazards
Ground
Ground
Shaking
Failure
Numbers of
Damage
Pipe Damage
and
Malfunction
Locations of
of
Pipe Damage
Equipment
Hydraulic Analysis
System Serviceability
Figure 1 Flowchart for the serviceability assessment
of water systems following earthquakes
2. PIPE DAMAGE MODELING
Repair rate (RR) is defined as the number of repairs
(or damages) per unit pipe length (km). It is widely
employed to indicate pipe fragility under seismic
effects. Numerous investigations have been made to
express the relationship between pipe repair rate and
earthquake-induced ground shaking (e.g. peak
ground acceleration, PGA) or ground failure (e.g.
permanent ground displacement, PGD). The pipe
material and diameter affect its repair rate, too. The
empirical formulae for pipe repair rates have been
proposed by the authors, which read (Liu et al.,
2011):
RR = C ⋅ RR 0
RR
0
where
RR PGA
RR PGD
= max[ RR ,RR ] + RR
PGA
=
= 0.6445 ⋅ PGD
PGDFault
−3
6.5756 × 10 ⋅ ( PGA −
0.728
PGDLiq
100)
0.878
⋅ p
where RR
0
is the standard pipe repair rate, C is
an adjustment coefficient and is a function of pipe
material and diameter, PGA and PGD are in
cm/sec 2 and cm, respectively. The terms
PGDFault
,
PGD
Liq
and p
Liq
represent the fault
rupturing and soil liquefaction-induced PGDs, and
the probability of occurrence of soil liquefaction,
respectively.
Conventionally, a stationary Poisson process is
widely used to simulate the damage locations along a
pipe. In this study, an approach based on the
expected number of damages of pipes was otherwise
proposed. From Figure 2, let the length of a typical
pipe segment be L . Assume there are a total of N
pipes in the water pipe network under study. Let all
pipes be broken down into segments of constant
length L from their beginning nodes (the length of
the last segment of each pipe may not equal L ), and
be denoted as ( i , j)
, where i refers to pipe i
( i = 1,..., N ) and j refers to its j -th segment. The
expected number of pipe damage of any pipe
segment ( i , j)
can be decided according to the
segment length and the corresponding pipe repair
Liq

ate. Denote this number as e ij
. Starting with the
origin of the number line, if all the expected numbers
of pipe damage e
11
, e12,...,
e21,
e22,...,
e NJ
(where
N
J
N
refers to the last segment of pipe N ) can be
sequentially accumulated as ( e 11
), ( e
11
+ e12
),
( e ),
11
+ e12
+ e13 ...,(
e
11
+ e12
+ ... + e NJ
) and denoted
N
on the number line, then the interval [ 0, E
R
] , where
E
R
equals to the summation of all the expected
numbers of pipe damage, consists of as many
sub-intervals as the number of all pipe segments with
lengths e
11
, e12,...,
e21,
e22,...,
e NJ
. This also means
N
that there exists a one-on-one mapping between any
real-number within [ 0, E
R
] and a specific pipe
segment.
were adopted in this study. This model includes pipe
break and various types of pipe leaks, and the
probability that each will occur in various pipe
materials, and also the hydraulic models and
parameters for each type of pipe damage. Following
their findings from water pipelines and their
damages in past earthquakes in the U.S., water pipe
materials could be classified into 5 types: cast iron,
ductile iron, jointed concrete, riveted steel and
welded steel. Furthermore, there are five different
types of pipe leaks, namely the annular
disengagement, round crack, longitudinal crack,
local loss of pipe wall, and local tear of pipe wall at
welded slip joint, as illustrated in Figure 3.
Conventional approach:
Assume that pipe damage follows a Poisson process
Proposed approach:
0
Accumulated
number of pipe
damage points
E R
Generate a random number within [0, E R ], designate the location, and repeat E R times
Figure 2 Comparison between the conventional and
the proposed approaches for simulating pipe damage
locations probabilistically
To simulate a location of damage along the pipe,
first, an arbitrary number between 0 and E
R
can be
generated using a random number generator that
follows uniform distribution. It will refer to one
single segment, say e nm
, along the axis of number
line. Finally, the midpoint of the m -th segment of
the n -th pipe is designated as a pipe damage
location. The same process can be repeated E R
times to determine all pipe damage locations.
The hydraulic models for pipe damages
proposed in GIRAFFE (Cornell University, 2008)
Figure 3 Schematic diagrams of the 5 types of pipe
leaks (Cornell University, 2008)
GIRAFFE further proposed the hydraulic models
for pipe breaks and leaks, respectively. A pipe break
and its hydraulic model can be depicted as the left
schematic diagram in Figure 4. At each of the broken
ends, a reservoir and a short pipe with a check valve
are needed being added to mimic the mechanism of
water flowing into the atmosphere. To take into
account the effect of a pipe break in simulation,
several steps to modify the hydraulic model of the
broken water system should be taken. They are: (1)
Decide the location and elevation of pipe break point,
(2) Remove the original link (pipe segment), (3) Add
two new nodes A and B at the location of pipe break
point, (4) Add two new links connecting the original

pipe segment ends to A and B, respectively, (5) Add
two new nodes A’ and B’ with the elevation of pipe
break point and designate them as reservoirs, and
finally (6) Add two new links connecting A-A’ and
B-B’ and specify them with one-way check valves.
Figure 5 Hydraulic model for a pipe leak (Cornell
University, 2008)
3. HYDRAULIC ANALYSIS AND NEGATIVE
PRESSURE ISSUE
Figure 4 Hydraulic model for a pipe break (Cornell
University, 2008)
On the other hand, a pipe leak and its hydraulic
model could be depicted as the right schematic
diagram in Figure 5. A pipe leak is hydraulically
equivalent to a sprinkler with a specific discharge
coefficient and an orifice size. This sprinkler is
further proven to be equivalent to a fictitious pipe
linking the original pipe and an added reservoir. A
check valve is designated to the fictitious pipe
ensuring that water flows from the leaking pipe to
the reservoir. The steps to modify the hydraulic
model of the leaking water system could be
summarized as follows: (1) Decide the location and
elevation of pipe leak point, (2) Remove the original
link (pipe segment), (3) Add a new node A at the
location of pipe leak point, (4) Add two new links
connecting the original pipe segment ends to A, (5)
Add a new node A’ with the elevation of pipe leak
point and designate it as a reservoir, and finally (6)
Add a new link connecting A and A’ and specify it as
a fictitious pipe with a diameter of corresponding
pipe leak model, and also specify it with a one-way
check valve.
Figure 6 depicts the schematic diagram of a
simplified water network. A water network system
usually consists of tanks, reservoirs, pumps, valves
and numerous pipes and nodes. The hydraulics of
such a system can be assumed as pressurized pipe
flows, and can be solved by using two sets of
equations (Rossman, 2000). Let there be N nodes,
NF fixed nodes (e.g. tanks and reservoirs) and K
pipes in a water network, then the first set prescribe
the difference of water head at the ends of each pipe
and read:
H − H
i
j
= h
ij
= r ⋅Q
n
ij
+ m ⋅Q
where H , h ,Q , r , n and m are the nodal head, head
loss, flow rate, resistance coefficient, flow exponent
and minor loss coefficient, respectively. The most
widely used empirical formulae for the pipe
resistance coefficient are the Darcy-Weisbach,
Hazen-Williams or Chezy-Manning equation, all of
which employ flow rate and various pipe parameters.
The second set prescribes the balance of flow at each
node and read:
∑
j
Q − D = 0
ij
i
2
ij

where
D
i
is the demand at node i . By using these
two sets of equations, the pipe flow can be solved in
terms of the water heads H
i
at N nodes and the
pipe flow rate Q (from node j to node i ) in
K pipes.
ij
(4) Perform hydraulic analysis using EPANET.
(5) Check the pressure at all nodes from the result of
Step (4) and, following the approach proposed by
Ballantyne et al. (1990) to eliminate the negative
pressure and summarize the water supply by
excluding the demands (supplies) at nodes of
negative pressure.
Read input file for the hydraulic
analysis of the water system
Figure 6 The schematic diagram of a simplified
hydraulic network (Rossman, 2000)
The procedure for assessing the post-earthquake
performance of a water system is illustrated in the
flowchart in Figure 7, which reads:
Modify input file according to
the simulated pipeline damage
Pipeline damage causes
any node disconnected
from the system network
YES
Remove the disconnected nodes
NO
(1) Read the input file for the hydraulic analysis of
the interested water system. This file is usually
prepared by the water utilities and is compatible
with the employed analysis software in terms of
data formatting. All attributes of the components
in the water system (e.g. reservoirs, tanks, pumps,
nodes and pipes) are defined in the file.
(2) Simulate the pipeline damage of the water system
based on an earthquake scenario. A pre-processor
has been developed in this study to decide the
locations and attributes of pipe breaks and leaks
in the pipeline network in a probabilistic way, and
then to modify the input file according to the
simulated pipeline damage. It takes into account
the seismic hazard and the pipe repair rate, and
the pipe damage models Proposed in GIRAFFE
(Cornell University, 2008) were employed.
(3) Check the connectivity of all nodes to the system
with simulated pipeline damage. Remove the
disconnected nodes by further modifying the
input file.
Pre-processor
Perform hydraulic
analysis using EPANET
Post-processor
Negative pressure
NO
occurs at any node
YES
Remove water supply at nodes of negative pressure
Evaluate the serviceability of the damaged water system
End
Figure 7 Flowchart for assessing post-earthquake
performance of a water system
While performing hydraulic analysis of a water
network with pipe damage, it is likely to predict
negative pressure at some nodes. Negative pressure
is generated due to the assumption that the pipe
flows are always full and pressurized. However,
water pipelines are not air-tight, especially when

they are damaged. As a result, hydraulic analysis of a
damaged water network tends toward overestimating
its ability to convey water. Elimination of negative
pressure under such circumstance is therefore
advised. In this study, the approach proposed by
Ballantyne et al. (1990), which assumes that no
water will flow through negative pressure nodes, was
employed in Step 5 of the assessment procedure.
Pipes
Junctions
Tanks or reservoirs
礁 溪 鄉
員 山 鄉
宜 蘭 市
頭 城 鎮
壯 圍 鄉
4. CASE STUDY
三 星 鄉
五 結 鄉
羅 東 鎮
The off-shore of eastern coast is one of the most
earthquake-prone areas in Taiwan region. In this
study, the water system in Yi-lan County, one of the
three counties in East Taiwan, was chosen as the test
bed for the implementation of the proposed ESLE
technology. The water system in Yi-lan County is
operated by the Eighth Branch of the Taiwan Water
Corporation. Its service area is 814 kilometer square.
The total pipe length is approximately 2,600 km. The
system serves 150,500 customers or 427,000 people,
with an average supply of 162,395 CMD (2010). The
major pipes include PVC pipes (63%), ductile iron
pipes (26%), HIWP (high-impact PVC) pipes (6%)
and cast iron pipes (1%). The entire system is
simplified as a hydraulic node-and-link network,
depicted in Figure 8, with a total of 358 nodes and
439 links.
Consider an earthquake occurring off-shore
Yi-lan County. The earthquake magnitude is 7.1, the
epicenter locates at the coordinates of ( 121.88
E,
24.28
N ) and the focal depth is 20km. Assume that
the source mechanism is a horizontal line source of
84.2km with north-south orientation. The ground
shaking and ground failure induced by this scenario
earthquake can be simulated by TELES and be
illustrated as Figure 9.
冬 山 鄉
蘇 澳 鎮
Figure 8 The water system in Yi-lan County
PGA
PGD ( 土 壤 液 化 )
PGA (g)
PGD (cm)
y
0.54 to 0.6
45 to 50
0.48 to 0.54
40 to 45
0.42 to 0.48
35 to 40
0.36 to 0.42
30 to 35
0.3 to 0.36
25 to 30
0.24 to 0.3
20 to 25
0.18 to 0.24
15 to 20
0.12 to 0.18
10 to 15
0.06 to 0.12
5 to 10
0 to 0.06
0 to 5 (
Figure 9 Simulated distribution of PGA (left) and
liquefaction-induced PGD (right) in Yi-lan County
under the M7.1 scenario earthquake
The Monte Carlo method was employed to
estimate the average post-earthquake serviceability
of the system. One hundred times of simulation were
performed, and the pipe breaks and leaks due to
ground shaking and failure were decided according
to a random process in each run. The simulation
results are depicted in Figure 10. Here, the
serviceability index (SI), defined as the ratio of flow
at demand nodes after and before an earthquake, is

used to quantify the system’s ability to meet the
demand in each town. Under this scenario, the worst
reduction in SI occurs in Tou-cheng (0.3521), while
the other two worst reductions occur in Zhuangwei
(0.5091) and Jiao-xi (0.5430), respectively.
Serviceability Index
0 to 0.1
0.1 to 0.2
0.2 to 0.3
0.3 to 0.4
0.4 to 0.5
0.5 to 0.6
0.6 to 0.7
0.7 to 0.8
0.8 to 0.9
0.9 to 1
1 to 1
礁 溪 鄉
頭 城 鎮
system in terms of the serviceability index (SI) of
each service area was simulated.
ACKNOWLEDGEMENT
The research funding from Water Resource Agency,
MOEA, Taiwan under Grants MOEA-WRA-
0990095 and MOEA-WRA-1000090 is gratefully
acknowledged. This research was made possible
through kind helps from the Taiwan Water
Corporation for providing technical assistance and
database.
員 山 鄉
宜 蘭 市
壯 圍 鄉
REFERENCES
三 星 鄉
五 結 鄉
羅 東 鎮
Ballantyne, D. B., Berg, E., Kennedy, J., Reneau, R.
and Wu, D. (1990). Earthquake Loss Estimation
大 同 鄉
冬 山 鄉
蘇 澳 鎮
Modeling of the Seattle Water System, Technical
Report, Kennedy/Jenks/Chilton, Federal Way, WA.
南 澳 鄉
Cornell University. (2008). GIRAFFE User’s
Manual, School of Civil & Environmental Eng.,
Cornell University, Ithaca, NY.
Figure 10 The simulated serviceability of Yi-lan’s
water system under the M7.1 scenario earthquake
5. CONCLUDING REMARKS
A technology for assessing the seismic performance
of water systems has been developed. Key issues
including models of strong motion attenuation and
pipe repair rate, and the pipe damage model have
explained. Particularly, a new approach for the
simulation of pipe damage locations based on the
expected number of damages of pipe segment has
been proposed. The water network system in Yi-lan
County, Taiwan was employed as a test bed for case
study. A major earthquake occurring off-shore was
considered. The post-earthquake performance of the
Liu, G.-Y., Chung, L.-L., Yeh, C.-H., Wang, R.-Z.,
Chou, K.-W., Hung, H.-Y., Chen, S.-A., Chen, Z.-H.
and Yu, S.-H. (2010). A Study on Pipeline Seismic
Performance and System Post-Earthquake Response
of Water Utilities (1/2), Technical Report MOEA-
WRA-0990095, Water Resource Agency, MOEA,
Taipei.
Liu, G.-Y., Chung, L.-L., Huang, C.-W., Yeh, C.-H.,
Chou, K.-W., Hung, H.-Y., Chen, Z.-H., Chou, C.-H.
and Tsai, L.-C. (2011). A Study on Pipeline Seismic
Performance and System Post-Earthquake Response
of Water Utilities (2/2), Technical Report MOEA-
WRA-1000090, Water Resource Agency, MOEA,
Taipei.

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